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### 11.24. Routh-Hurwitz Criterion

The Routh-Hurwitz criterion determines stability of the system on the basis of the location of roots of a characteristic equation with respect to the imaginary axis of the s-plane without actually solving the equation. This gives just a qualitative result and is the fastest method to know just about the stability of the system. The procedure to be adopted for the application of this criterion is as follows:

 1 Determine the characteristic equation of the system. 2 If it has any fractional terms, then multiply the characteristic equation by the denominator so that there is no fractional term. 3 Arrange the resulting equation in descending power of ‘s’ with the leftmost term being of the highest power. 4 It must ...

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